Let T : R 2 → R 2 be the linear transformation defined by T ( [ x 1 x 2 x 3 ] ) = [ x 1 + 2 x 2 + 4 x 3 2 x 1 + 3 x 2 + 5 x 3 ] Which of the following vectors are in null space of T . a) [ 0 0 0 ] b) [ 2 − 3 1 ] c) [ 1 2 1 ] d) [ − 1 3 / 2 − 1 / 2 ]
Let T : R 2 → R 2 be the linear transformation defined by T ( [ x 1 x 2 x 3 ] ) = [ x 1 + 2 x 2 + 4 x 3 2 x 1 + 3 x 2 + 5 x 3 ] Which of the following vectors are in null space of T . a) [ 0 0 0 ] b) [ 2 − 3 1 ] c) [ 1 2 1 ] d) [ − 1 3 / 2 − 1 / 2 ]
Solution Summary: The author explains how to find the vectors in the null space of T.
Let
T
:
R
2
→
R
2
be the linear transformation defined by
T
(
[
x
1
x
2
x
3
]
)
=
[
x
1
+
2
x
2
+
4
x
3
2
x
1
+
3
x
2
+
5
x
3
]
Which of the following vectors are in null space of
T
.
a)
[
0
0
0
]
b)
[
2
−
3
1
]
c)
[
1
2
1
]
d)
[
−
1
3
/
2
−
1
/
2
]
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY